A _____ shows how an object changes from one state to another, depending on events that affect the object.

a. ​scatter diagram
b. ​state transition diagram
c. ​business process diagram
d. ​case tools diagram

The measure of angle x is 70°.

Here we have the image of some triangles, and we want to find the value of the interior angle x in the left triangle.

What you need to remember here is that the sum of the interior angles of any triangle is always equal to 180°.

Then, for the left triangle, we can write:

30° + 80° + x° = 180°

Now we can solve that equation for x, then we will get:

x° = 180° - 80° - 30°

x = 70°

That is the measure of angle x.

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Answer:

2√7+9√3

Step-by-step explanation:

just add the ones with the same radicands

Answer:

Step-by-step explanation:

      =2(5)^2 - 5(7)

      = 2(25) - 35

      = 50 - 35

      = 15

The zeros of the polynomial are: , 3, and -23/2. Therefore, the y-intercept is (0, -15).

From the given information, we know that x= and x=3 are two zeros of the polynomial f(x) = 2x³ – 9x² + 17x – 19x – 15.

To find the remaining complex zeros, we can use polynomial long division or synthetic division. However, we first need to use the two zeros to factor the polynomial.

We can start by writing the polynomial in factored form as:

f(x) = (x - )(x - 3)(ax + b)

where (ax + b) represents the remaining factor.

To find the values of a and b, we can expand the above expression and compare the coefficients with the original polynomial:

f(x) = (x - )(x - 3)(ax + b)

= (ax² + bx - 3ax - 3b)x + (3abx - ab)

= (a)x³ + (b - 3a)x² + (3a - b)x - 3b

Comparing coefficients with the given polynomial, we get:

a = 2

b - 3a = 17

3a - b = -19

-3b = -15

Solving for these equations, we get:

a = 2

b = 23

Therefore, the remaining factor is (2x + 23).

Thus, the complete factorization of the polynomial is:

f(x) = (x - )(x - 3)(2x + 23)

Now, we can find the zeros of the polynomial by setting each factor equal to zero:

x - = 0 => x =

x - 3 = 0 => x = 3

2x + 23 = 0 => x = -23/2

Hence, the zeros of the polynomial are: , 3, and -23/2.

To sketch the graph of the polynomial, we can plot the x-intercepts (, 3, and -23/2) on the x-axis and the y-intercept (which we can find by setting x = 0) on the y-axis.

When x = 0, we get:

f(0) = 2(0)³ - 9(0)² + 17(0) - 19(0) - 15

= -15

Therefore, the y-intercept is (0, -15).

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The derivative of the function at the point p in the direction of a is 71/7.

option A.

The derivative of the function is calculated as follows;

Df(p, a) = f(p) · a

where;

The given function;

f(x, y, z) = 7x - 10y + 5z, p= (4,2,5), a = 3/7 i – 6/7- 2/7 k

The gradient of the function, f is calculated as;

f(x, y, z) = (δf/δx, δf/δy, δf/δz)

The partial derivatives of f with respect to each variable is calculated as;

δf/δx = 7

δf/δy = -10

δf/δz = 5

The gradient of the function f is ;

f(x, y, z) = (7, -10, 5)

Df(p, a) = f(p) · a

Df(p, a)  = (7, -10, 5) · (3/7, -6/7, -2/7)

Df(p, a) = (7 ·3/7) + (-10 · -6/7) + (5 · -2/7)

Df(p, a)  = 3 + 60/7 - 10/7

Df(p, a)  = 71/7

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The perimeter of the triangles are 12m and 16.2m.

Perimeter is a term used in geometry to refer to the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is commonly used to describe the "outer boundary" or "circumference" of a shape

According to the given information:

In the first triangle ABC, given that AB=5m and ∠B=53°.

By using trigonometric function,

sin 53° = \(\frac{opp}{hyp}\)

0.7986 = \(\frac{AC}{5}\)

AC = 3.993 ≈ 4

Cos 53° = \(\frac{adj}{hyp}\)

0.601 = \(\frac{CB}{5}\)

CB = 3.005 ≈ 3

Perimeter = 3+4+5 = 12m

In the second triangle ABC, given that AC=4.5m and ∠B=42°.

By using trigonometric function,

sin 42° = \(\frac{opp}{hyp}\)

0.6691 = \(\frac{4.5}{AB}\)

AB = 6.725 ≈ 6.7

cos 42° = \(\frac{BC}{AB}\)

0.7431 = \(\frac{BC}{6.7}\)

BC = 4.97 ≈ 5

Perimeter = 5+6.7+4.5 ≈ 16.2

The perimeter of the two triangles are 12m and 16.2m

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The area between the singles and doubles sidelines in tennis is called the tramlines. Tramlines serve specific purposes and affect the rules and strategies of the game.

The tramlines, also known as alleyways or doubles alleys, are located on both sides of the tennis court, running parallel to the singles sidelines. They create additional playing areas for doubles matches, extending the width of the court. These tramlines are marked by lines that are typically one and a half feet wide.

During doubles play, each team member has their own respective tramline. The purpose of the tramlines is to define the legal hitting areas for players. When serving, the server must aim to hit the ball within the singles sideline and the tramline on their side of the court. After the serve, the ball is considered "in" if it lands within the tramlines and between the singles and doubles sidelines.

The presence of the tramlines influences the strategies and tactics used in doubles matches. Players can utilize the additional space to angle shots and create different angles for their opponents to cover. The tramlines also affect positioning and movement on the court, as players need to cover a wider area during rallies.

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The y intercept is 0 and rate of change is 0.25 of the given function.

The function tells the relation between a collection of inputs, each having an output.

Given that, the late fees for a school library are represented by the function c = 0.25d, where c is the total cost and d is the number of days a book is late.

The slope intercept form of an equation is given by,

y = mx + c

Where, m is the slope and c is the constant,

The given equation is,

c = 0.25d

On comparison with slope intercept form, we get,

m = 0.25,

c = 0

We know that, the rate of change is given by the slope of the line and y intercept is given the constant.

Hence, rate of change is 0.25 and y intercept is 0

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Answer:

mean: 8

Step-by-step explanation:

Find the sum of all of the numbers:

3+4+5+7+10+12+15=56

Divide the sum by the quantity of numbers in the set:

56/7=8

Answer:

The mean= 8

Acellus sux

Step-by-step explanation:

The zero of the function f(x) = x - 4 is 4

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 4

By definition, the zero of the function is the point where the fucnction has a value of 0

i.e. f(x) = 0

When the value f(x) = 0 is substituted in the above equation, we have the following equation

x - 4 = 0

Add 4 to both sides

So, we have

x - 4 + 4 = 0 + 4

Evaluate the sum

x = 4

Hence, the zero of the function is 4

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

The equations of the normal plane and osculating plane of the curve at the given point are given by N = 0 and O = 0.

Here is the step-by-step explanation for finding equations of the normal plane and osculating plane of the curve at the given point for X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and 150:

Given that X= sin 2t, y=-c0s 2t, z =(0, 1, 2x) and t = 150.

Let us first find the first derivative of the given function.

f (t) = [X(t), Y(t), Z(t)] = [sin 2t, -cos 2t, 2 sin 2t]f'(t) = [2 cos 2t, 2 sin 2t, 4 cos 2t]

Again, let us find the second derivative of the given function.

f''(t) = [-4 sin 2t, 4 cos 2t, -8 sin 2t]At t = 150, we have

f'(t) = [2 cos 300, 2 sin 300, 4 cos 300] = [-1, √3, 2]f''(t) = [-4 sin 300, 4 cos 300, -8 sin 300] = [-2 √3, -2, 4 √3]

At the given point [X(150), Y(150), Z(150)] = [sin 300, -cos 300, 2 sin 300] = [√3/2, -1/2, √3]

The equation of the normal plane can be found as

N(x, y, z) = [f'(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0

The equation of the osculating plane can be found as

O(x, y, z) = [f''(150)] . [x - X(150), y - Y(150), z - Z(150)] = 0[-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0

Hence, the equations of the normal plane and osculating plane of the curve at the given point are given by

N(x, y, z) = [-1, √3, 2] . [x - √3/2, y + 1/2, z - √3] = 0and O(x, y, z) = [-2√3, -2, 4√3] . [x - √3/2, y + 1/2, z - √3] = 0 respectively.

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Answer:

Find the GCD (or HCF) of numerator and denominator

GCD of 63 and 9 is 9

Divide both the numerator and denominator by the GCD

63 ÷ 9

9 ÷ 9

Reduced fraction:  

7/1

Therefore, 63/9 simplified to lowest terms is 7/1.

Step-by-step explanation:

The factorize expression of 25x²-4x²-9 is 3(7x²-3).

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

We have the quadratic function,

25x²-4x²-9.

To factorize the function:

First, combine similar terms,

25x²-4x²-9,

= 21x²-9.

Now, factor out the common factor.

That means,

3(7x²-3).

Therefore, the required function is 3(7x²-3).

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The set representing the equivalence relation r can be written as:

r = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (e, e)}

Based on the given information, an equivalence relation r on the set A = {a, b, c, d, e} with two equivalence classes. Know that ard, brc, and erd.

To write out the equivalence relation r as a set, we can list all the ordered pairs that belong to the relation.

The equivalence relation r consists of all the ordered pairs (x, y) such that x and y are related (i.e., belong to the same equivalence class). Since we have two equivalence classes, let's denote them as [a] and [e].

The equivalence class [a] contains the elements a, b, and c, and the equivalence class [e] contains the element e.

Thus, the set representing the equivalence relation r can be written as:

r = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (e, e)}

Each ordered pair represents a relation between two elements in the set A based on the given equivalence relation r.

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Answer:

The six consecutive integers would be:

28, 29, 30, and 31, 32, 33, which, indeed total to 183, and the largest, obviously, is 33.

Step-by-step explanation:

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Answer: 28, 29, 30,31,32,33

Step-by-step explanation: To know the sum of integers, let the first integer is n.

Given, 6 consecutive integers. which means: n, n+1, n+2, n+3, n+4, n+5

Also given,

n + n+1+ n+2 + n+3 + n+4 + n+5 = 183

= n+ n+n+n+n+n+ 1+2+3+4+5= 183

= 6n+15 =183

= 6n = 183-15       (168)

= n = 168/6

= n = 28

So, as per the formula, n is 28 then 6 consecutive integers are 29, 30, 31, 32, 33.

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The equation that represents the graph is y = -(2/3)x + 6 .

The X- intercept is defined as the point at which the line crosses the x axis.

The Y- intercept is defined as the point at which the line crosses the y axis.

When a and b are the x and y intercept of a line then

the equation of line in intercept form is x/a + y/b = 1 .

Form the graph in the question

we can see that the graph crosses the x axis at 9, so it's x intercept is 9.

and the graph crosses the y axis at 6, so it's y intercept is 6.

So the intercept form of the line will be given by

x/9 + y/6 = 1

taking LCM of 6 and 9 as 18 ,

and solving further we get ,

2x/18 + 3y/18 = 1

(2x + 3y)/18 = 1

2x + 3y = 18

3y = 18 - 2x

Dividing both sides by 3 , we get

y = 18/3 - (2/3)x

y = 6 - (2/3)x

y = -(2/3)x + 6

Therefore , the equation that represents that represents the graph is                  y = -(2/3)x + 6 .

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Answer:

cube root of volume

Step-by-step explanation:

Given an arithmetic sequence with a common difference of 3 and the tenth term being 11, we can find the sum of the first 30 terms. The sum is 810.

In an arithmetic sequence, each term is obtained by adding a constant value, called the common difference, to the previous term. Let's denote the first term of the sequence as 'a' and the common difference as 'd'.

Given that the tenth term is 11 and the common difference is 3, we can use this information to find the first term. We know that the tenth term is obtained by adding the common difference 9 times to the first term:

a + 9d = 11

Substituting the value of the common difference (d = 3), we can solve for 'a':

a + 9(3) = 11

a + 27 = 11

a = 11 - 27

a = -16

Now that we have the first term 'a' and the common difference 'd', we can find the sum of the first 30 terms using the formula for the sum of an arithmetic series:

S = (n/2)(2a + (n-1)d)

Here, 'n' represents the number of terms. Substituting the values, we have:

S = (30/2)(2(-16) + (30-1)(3))

S = 15(-32 + 29(3))

S = 15(-32 + 87)

S = 15(55)

S = 825

Therefore, the sum of the first 30 terms of the given arithmetic sequence is 810.

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The total fabrics used on a headband and wristband for each player is 33.47 inches

Fabrics used per person on headbands = 784.96 inches / 32 persons

= 24.53 inches

Fabrics used per person on wristbands = 250.32 inches / 28 persons

= 8.94 inches

Total fabrics used per person = Fabrics used per person on headbands + Fabrics used per person on wristbands

= 24.53 inches + 8.94 inches

= 33.47 inches

In conclusion, the total fabrics used per person is 33.47 inches

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By applying Newton's method with an initial interval [a, b] obtained from the interval division method, we can find an approximate solution after three iterations.

(3-1-1) The interval division method involves dividing the range 3-1 into intervals of length 1. We then analyze the function f(x) = In(z) - 5 + z within each interval to determine if there are solutions. By sketching or graphing the function, we can observe where it intersects the x-axis and identify the intervals that contain solutions.

(3-1-2) Newton's method algorithm to solve the equation f(x) = In(z) - 5 + z involves the following steps:

1. Choose an initial guess x₀ within the interval [a, b] obtained from the interval division method.

2. Iterate using the formula xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ), where f'(x) represents the derivative of f(x).

3. Repeat the iteration process until convergence is achieved or a desired level of accuracy is reached.

(3-1-3) Using Newton's method with an initial interval [a, b] obtained from the interval division method, we start with an initial guess x₀ within that interval. After three iterations of applying the Newton's method formula, we obtain an approximate solution by refining the initial guess. The results will be given in four decimal places, providing an approximation for the solution within the specified interval and accuracy level.

Please note that since the specific values for the intervals [a, b] and the equation f(x) = In(z) - 5 + z are not provided, the actual calculations and results cannot be determined without specific values for the variables involved.

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Answer:

18 cm

Step-by-step explanation:

Let's assume that the length of the stick is x cm.

Then, the lengths of pieces A, B and C would be 2x/10 cm, 3x/10 cm, and 5x/10 cm respectively.

Since C is longer than B by 8 cm, the length of C is 3x/10 + 8 cm, and the length of B is 3x/10 cm.

Therefore, the total length of the stick would be:

x = 2x/10 + 3x/10 + (3x/10 + 8)

x = 10x/10 + 8

x = 10 + 8

x = 18 cm

So, the length of the stick is 18 cm.

Answer: 20 cm

Step-by-step explanation:

create an equation.

2x : 3x : 5x

We are also told C is longer than B by 8 cm. So,

A : x : x+8

If 5x = x+8, solve for this: 4x = 8 so x =2.

Now, we can plug back in the original values.

2(2) + 3(2) + 5(2) = 20.

the stick is 20 centimeters long.

The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

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Answer: 48.75

Step-by-step explanation:

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Null hypothesis states, the new incentive program will not have a significant effect on reducing employee sick leave (26%). The new incentive program will result in a significant reduction in employee sick leave (26%), alternative hypothesis.

Hypothesis testing typically involves determining the statistical significance of the observed data by comparing it to a null hypothesis.

The null hypothesis (H0) in this scenario could be stated as: "The introduction of the new incentive program for perfect attendance will not have a significant effect on reducing employee sick leave (26%)."

The alternative hypothesis (H1) would then be: "The introduction of the new incentive program for perfect attendance will result in a significant reduction in employee sick leave (26%)."

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To find a basis for the subspace spanned by the vectors V1 = (1, 0, 0), V2 = (1, 0, 1), V3 = (4, 0, 1), and V4 = (0, 0, -2), we need to determine which combinations of these vectors are linearly independent.

We can do this by performing row operations on the augmented matrix [V1 | V2 | V3 | V4] and checking for the presence of a row of zeros. If a row of zeros is found, then the corresponding vectors are linearly dependent.

Let's construct the augmented matrix and perform row operations:

[ 1 1 4 0 ]

[ 0 0 0 0 ]

[ 0 1 1 -2 ]

Performing row operations, we obtain:

[ 1 1 4 0 ]

[ 0 1 1 -2 ]

[ 0 0 0 0 ]

From the row of zeros, we can see that the vectors V1, V2, V3, and V4 are linearly dependent. Therefore, a basis for the subspace spanned by these vectors will consist of only linearly independent vectors.

In this case, the basis for the subspace is formed by V1 and V3. Thus, V1 and V3 form a basis for the subspace spanned by {V1, V2, V3, V4}.

Therefore, the correct answer is: V1 and V3 form a basis for span {V1, V2, V3, V4}.

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Answer:

30 inches

Step-by-step explanation:

Length of road A = 1¼ miles

Length of road A on map = 1½ inches

Unit rate for inches per miles on the map = 1½ inches ÷ 1¼ miles = ³/2 ÷ ⁵/4 = ³/2 × ⅘ = ⁶/5 inches per mile

Length big Road B on map:

Road B actual length = 10 miles

Thus, using the unit rate of ⁶/5 inches to 1 mile, length of road B on map would be calculated as shown below:

⁶/5 × 10 = 6*5 = 30 inches

Road B is 30 inches long on the map.

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation: